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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Towards a Quantum Algorithm for the Incompressible Nonlinear Navier-Stokes Equations

In this work, we present novel concepts for quantum algorithms to solve transient, nonlinear partial differential equations (PDEs). The challenge lies in how to effectively represent, encode, process, and evolve the nonlinear system of PDEs on quantum computers. We will discuss the new techniques using the incompressible Navier-Stokes equations as an example, because it represents the fundamental nonlinear feature and yet removes certain complexity in physics, allowing us to focus on the design of quantum algorithms. Previous attempts solving nonlinear PDEs in quantum computation have often involved storing multiple copies of solutions or employing linearizations. Neither is practical due to exponential scaling with evolution time or insufficient solution accuracy. We propose a new framework based on matrix product states (MPSs) and matrix product operators (MPOs), in addition to the Krylov subspace methods. For example, the solution variables of the Navier-Stokes equations are represented by MPSs, and the linear and nonlinear terms are processed by MPOs. The time evolution of the operators is attained by a fast-forwarding algorithm using Krylov subspace methods. Furthermore, we discuss various techniques for efficient encoding of MPSs, measurement reduction for MPOs, and use of tensor operations to treat multi-variate, multi-physics characteristics of Navier-Stokes.

Gopalakrishnan Meena, Murali [ORNL] (ORCID:0000000↗
DOE OSTI2026

A Scalable Reduced‐Order Model for the Steady Navier–Stokes Equations

Scaling up new scientific technologies from laboratory to industry often involves demonstrating performance on a larger scale. Computer simulations can accelerate design and predictions in the deployment process, though traditional numerical methods are computationally intractable even for intermediate pilot plant scales. Recently, the component reduced order modeling method has been developed to tackle this challenge by combining projection reduced order modeling and discontinuous Galerkin domain decomposition. However, while many scientific or engineering applications involve nonlinear physics, this method has only been demonstrated for various linear systems. In this work, the component reduced order modeling method is extended to steady Navier–Stokes flow, with application to general nonlinear physics in view. The large‐scale, global domain is decomposed into a combination of small‐scale unit component. Linear subspaces for flow velocity and pressure are identified via proper orthogonal decomposition over sample snapshots collected from each small‐scale unit component. Velocity bases are augmented with a pressure supremizer to satisfy the inf–sup condition for stable pressure prediction. Two different nonlinear reduced order modeling methods are employed and compared for efficient evaluation of nonlinear advection: A third‐order tensor projection operator and the empirical quadrature procedure. The proposed method is demonstrated on the flow over arrays of five different unit objects, achieving a 23‐fold speedup with less than 4% relative error in domains up to 256 times larger than the unit components. Furthermore, a numerical experiment with the pressure supremizer strongly indicates the need for a supremizer for stable pressure prediction. A comparison between the tensorial approach and the empirical quadrature procedure revealed a slight advantage of the empirical quadrature procedure. The framework is compared with an alternating Schwarz‐based reduced‐order approach, demonstrating improved efficiency and robustness for the DG‐based global solver while retaining flexibility for sub‐scale iterative solvers. The method is further extended to a coupled advection–diffusion and Navier–Stokes system, illustrating its applicability to multi‐physics problems and its potential for more general, inter‐coupled nonlinear systems.

42 ENGINEERING↗
DOE OSTI2024

Note on two formulations of Crank-Nicolson method for Navier-Stokes equations

Here, we consider two formulations of the Crank-Nicolson (CN) method for the Navier-Stokes equations (NSE). The “natural” way of implementing CN for NSE is formally second order accurate in time for both velocity and pressure, whereas another formulation approximates pressure with only first order accuracy in time. Both versions of the method are applied to the benchmark problem of computing drag and lift in the flow around a cylinder. We show that the presumably more accurate version of the CN can create a solution with nonphysical oscillations and give incorrect predictions for the maximal drag coefficient, whereas the other formulation of the method predicts the drag and lift coefficients more accurately and does not introduce nonphysical oscillations. We locate the source of the issue and suggest several remedies.

Crank-Nicolson↗
DOE OSTI2024

A second-order-in-time, explicit approach addressing the redundancy in the low-Mach, variable-density Navier-Stokes equations

A novel algorithm for explicit temporal discretization of the variable-density, low-Mach Navier-Stokes equations is presented here in this study. Recognizing there is a redundancy between the mass conservation equation, the equation of state, and the transport equation(s) for the scalar(s) which characterize the thermochemical state, and that it destabilizes explicit methods, we demonstrate how to analytically eliminate the redundancy and propose an iterative scheme to solve the resulting transformed scalar equations. The method obtains second-order accuracy in time regardless of the number of iterations, so one can terminate this subproblem once stability is achieved. Hence, flows with larger density ratios can be simulated while still retaining the efficiency, low cost, and parallelizability of an explicit scheme. The temporal discretization algorithm is used within a pseudospectral direct numerical simulation which extends the method of Kim, Moin, and Moser for incompressible flow to the variable-density, low-Mach setting, where we demonstrate stability for density ratios up to ~25.7.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

A fourth order sharp immersed method for the incompressible Navier-Stokes equations with stationary and moving boundaries and interfaces

We propose a fourth order Navier-Stokes solver based on the immersed interface method (IIM), for flow problems with stationary and one-way coupled moving boundaries and interfaces. Our algorithm employs a Runge-Kutta-based projection method that maintains high-order temporal accuracy in both velocity and pressure for steady and unsteady velocity boundary conditions. Fourth order spatial accuracy is achieved through a novel fifth order IIM discretization scheme for the advection term, as well as existing high-order interface-corrected finite difference schemes for the other differential operators. Using a set of manufactured flow problems with stationary and moving boundaries, we demonstrate fourth order convergence of velocity and pressure in the infinity norm, both inside the domain and on the immersed boundaries. The solver’s performance is further validated through a range of practical flow simulations, highlighting its efficiency over a second order scheme. Finally, we showcase the ability of our immersed discretization scheme to handle interface-coupled multiphysics problems by solving a conjugate heat transfer problem with multiple immersed solids. Overall, the proposed approach robustly combines the efficiency of high order discretization schemes with the flexibility of immersed discretizations for flow problems with complex, moving boundaries and interfaces.

42 ENGINEERING↗
DOE OSTI2024

Thermodynamically consistent Cahn–Hilliard–Navier–Stokes equations using the metriplectic dynamics formalism

Cahn–Hilliard–Navier–Stokes (CHNS) systems describe flows with two-phases, e.g., a liquid with bubbles. Obtaining constitutive relations for general dissipative processes for such systems, which are thermodynamically consistent, can be a challenge. We show how the metriplectic 4-bracket formalism (Morrison and Updike, 2024) achieves this in a straightforward, in fact algorithmic, manner. First, from the noncanonical Hamiltonian formulation for the ideal part of a CHNS system we obtain an appropriate Casimir to serve as the entropy in the metriplectic formalism that describes the dissipation (e.g. viscosity, heat conductivity and diffusion effects). General thermodynamics with the concentration variable and its thermodynamics conjugate, the chemical potential, are included. Having expressions for the Hamiltonian (energy), entropy, and Poisson bracket, we describe a procedure for obtaining a metriplectic 4-bracket that describes thermodynamically consistent dissipative effects. The 4-bracket formalism leads naturally to a general CHNS system that allows for anisotropic surface energy effects. Furthermore, this general CHNS system reduces to cases in the literature, to which we can compare.

Cahn–Hilliard↗
DOE OSTI2025

Reaction-induced departures from continuum Navier–Stokes turbulence

Reactive hydrodynamic turbulence is an inherently multiscale phenomenon, characterized by the separation between energy-containing, viscous, and molecular length and time scales. The separation between the viscous scale (the Kolmogorov scale) and the molecular mean free path ostensibly justifies a macroscopic description of reactive turbulence via the Navier–Stokes (NS) equations. However, here we use molecular-level simulations to demonstrate that exothermic bimolecular reactions can cause the NS description of turbulence to break down in the near-continuum regime. Sufficiently energetic heat-releasing reactive collisions strongly distort the Maxwell–Boltzmann velocity distribution function, modifying not only the macroscopic chemical rate law but the kinetic-energy-transfer processes as well. This translational nonequilibrium ultimately introduces significant departures from the NS description in the kinetic energy spectra at scales orders of magnitude larger than both the molecular mean free path and the Kolmogorov length scale. These departures prove substantial enough to meaningfully alter integrated quantities, including the overall turbulence kinetic energy itself.

molecular gas dynamics↗
DOE OSTI2026

Large Eddy Simulation of Low-Reynolds-Number Turbulent Flow of Low-Prandtl-Number Fluid in a Tight Lattice Bundle for Assessment of Reynolds-Averaged Navier-Stokes Turbulence Model

The MARVEL (Microreactor Applications Research Validation and Evaluation) microreactor utilizes natural circulation as core cooling mechanism and liquid metal as a primary coolant. Moreover, the reactor core has a pitch-to-diameter ratio of 1.056, which is considered a tight lattice configuration. Numerous studies have widely reported that Reynolds-Averaged Navier-Stokes (RANS) turbulence models inaccurately predict heat transfer in liquid metals and fail to capture flow pulsations that can occur within tight lattices, leading to further inaccuracies in simulation results. Therefore, evaluating the accuracy of RANS turbulence models in the thermal-hydraulic analysis of the MARVEL microreactor core is crucial for assessing reactor safety. In this study, a Large Eddy Simulation (LES) of the MARVEL microreactor core subchannel was conducted and compared with a RANS simulation to evaluate the accuracies and conservatism of the RANS model. The flow pulsation in a tight lattice predicted by LES enhanced the heat transfer, whereas the RANS model underpredicted it. Consequently, the RANS model predicted the peak cladding temperature higher than the LES model, but the discrepancy between the two approaches was not significant due to the good thermal characteristics of the liquid metal. It can be concluded that the steady-state RANS model is effective for the thermal analysis of liquid-metal-cooled MARVEL microreactor core and can provide conservative predictions from a safety analysis perspective.

21 - SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLAN↗
DOE OSTI2024

ECAR-7932 Rev 0 Large Eddy Simulation of MARVEL Reactor Core Subchannel to Evaluate Model Uncertainty of Reynolds-Averaged Navier-Stokes Equation Based Computational Fluid Dynamics Analysis

In the previous work (ECAR-7210), the peak cladding temperature of the MARVEL microreactor has been evaluated by steady-state Reynolds-Averaged Navier-Stokes (RANS) based computational fluid dynamics (CFD) simulations. Although numerical uncertainties of RANS-based CFD simulations has been assessed in ECAR-7210, the model uncertainty of RANS turbulence models must be investigated to resolve the issues related to inaccurate prediction of turbulent heat flux and flow pulsation in a tight lattice rod bundle using the steady-state RANS simulations. Consequently, this ECAR conducted a high-fidelity CFD analysis utilizing Large Eddy Simulation (LES) to generate reference data and investigated the model uncertainty of RANS-based CFD simulations.

21 - SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLAN↗
DOE OSTI2025

Metriplectic four-bracket algorithm for constructing thermodynamically consistent dynamical systems

A unified thermodynamic algorithm is presented for constructing thermodynamically consistent dynamical systems, i.e., systems that have Hamiltonian and dissipative parts that conserve energy while producing entropy. The algorithm is based on the metriplectic 4-bracket given in Morrison and Updike [Phys. Rev. E 109, 045202 (2024)]. A feature of the unified thermodynamic algorithm is the force-flux relation 𝐉 𝛼 =−𝐿 𝛼⁢𝛽 𝛁(𝛿⁢𝐻⁡/𝛿⁢𝜉 𝛽 ) for phenomenological coefficients 𝐿 𝛼⁢𝛽 , Hamiltonian 𝐻, and dynamical variables 𝜉 𝛽 . The algorithm is applied to the Navier-Stokes-Fourier, the Cahn-Hilliard-Navier-Stokes, and Brenner-Navier-Stokes-Fourier systems, and significant generalizations of these systems are obtained.

Multiphase flows↗
DOE OSTI2024

Posterior comparison of model dynamics in several hybrid turbulence model forms

Hybrid turbulence models that can accurately reproduce unsteady three-dimensional flow physics across the entire range of grid scales and turbulence dynamics from Reynolds-averaged Navier–Stokes (RANS), through large-eddy simulation (LES), down to direct numerical simulations (DNS) are of increasing interest to the turbulence modeling community. However, despite decades of research and development, the basic tasks of eliminating poor-performing hybrid RANS-LES models and accelerating adoption of superior models through well-designed validation and verification have yet to occur. As a step in this direction, in this work we evaluate thirteen different hybrid RANS-LES models via systematic grid refinement of decaying homogeneous isotropic turbulence. We further derive a novel mathematical framework for assessing the energy partitioning dynamics of each Hybrid RANS-LES model, wherein model-to-model variations in energy partitioning can be interpreted as different feedback mechanisms operating on a low-dimensional nonlinear dynamical system. We found that model forms similar to the flow simulation methodology—also often termed very-large eddy simulation—are dynamically inconsistent with DNS at all resolutions. Additionally, we found a strong dynamical similarity in the feedback mechanisms of all models related to detached eddy simulation and partially averaged Navier–Stokes that is inherent to their general model forms.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗